Just an update.
I plugged the frig back in so I could look at the defrost patterns, as Samurai Appliance Repair Man suggested.
The freezer steadily got warmer and warmer, as did the frig. Finally it was no longer keeping any sort of cooling.
It appears that there is a sealed system problem. This was confirmed by the repair person, who estimated $600+ to fix. He recommended replacement.
This frig is not all that old and it still looks great. Seems like a pity to junk it. By comparison, before I always had really old refrigerators and never had any problems with them. *shrug* Fortunately I have a beer frig to use while waiting on a new frig delivery. The beer frig is harvest gold, which should give you some hint about how old it is.
Thank you all so much for your assistance. Although I wasn't able to fix my frig, I enjoyed learning more about the diagnostic process and the components involved.